High temperature spiral snake superconducting resonator having wider runs with higher current density

ABSTRACT

Novel structures and methods for forming useful high temperature superconducting devices, most particularly resonators, are provided. Structures resulting in reduced peak current densities relative to known structures achieve numerous desirable benefits, especially including the reduced intermodulation effects of earlier resonators. In one aspect of this invention, a spiral in, spiral out resonator is provided, characterized in that it has an odd number of long runs, at least equal to five long runs, where the long runs are connected by turns, and wherein there are at least two sequential turns of the same handedness, followed by at least two turns of the opposite handedness. In yet another aspect of this invention, it has been discovered that reducing the size of the input and output pads of HTS resonators increases the relative inductance compared to the capacitance. Yet another resonator structure is a spiral snake resonator having a terminal end disposed within the resonator. A wide in the middle structure and wide at peak current density resonator structures utilize enlarged width portions of the resonator in those areas where current density is largest. In yet another aspect of this invention, operation of resonators in high modes, above the fundamental mode, reduce peak current densities. Resonators operated in modes in which current in adjacent long runs are in the same direction further serve to reduce current densities, and intermodulation effects. Symmetric current structures and modes of operation are particularly advantageous where far field effects are compensated for.

RELATED APPLICATION

This application is a continuation of application Ser. No. 10/167,938,filed Jun. 10, 2002, now issued as U.S. Pat. No. 6,895,262 which is acontinuation of application Ser. No. 09/460,274, filed Dec. 13, 1999,now issued as U.S. Pat. No. 6,424,846, which is a continuation ofapplication Ser. No. 08/885,473, filed on Jun. 30, 1997, issued as U.S.Pat. No. 6,026,311, which is a continuation-in-part of application Ser.No. 08/826,435 (224/302), filed Mar. 20, 1997, now abandoned, which is acontinuation of application Ser. No. 08/297,289, filed Aug. 26, 1994,entitled “Lumped Element Filters”, issued as U.S. Pat. No. 5,616,539,which is in turn a continuation-in-part of application Ser. No.08/070,100 filed May 28, 1993, entitled “Lumped High TemperatureSuperconductor Lumped Elements and Circuits Therefrom” (as amended),issued as U.S. Pat. No. 5,618,777 on Apr. 8, 1997.

FIELD OF THE INVENTION

This invention relates to structures and methods formed from hightemperature superconductors. More particularly, it relates to devicessuch as resonators having high Q and reduced intermodulation distortionfor use as passive microwave devices.

BACKGROUND OF THE INVENTION

Electrical components come in various conventional forms, such asinductors, capacitors and resistors. A lumped electrical element is onewhose physical size is substantially less than the wave length of theelectromagnetic field passing through the element. A distributed elementis one whose size is larger than that for a lumped element. As anexample, a lumped element in the form of an inductor would have aphysical size which is a relatively small fraction of the wave lengthused with the circuit, typically less than ⅛ of the wavelength.

Inductors, capacitors and resistors have been grouped together intouseful circuits. Useful circuits including those elements includeresonant circuits and filters. One particular application has been theformation of filters useful in the microwave range, such as above 500MHZ.

Considering the case of conventional microwave filters, there have beenbasically three types. First, lumped element filters have usedseparately fabricated air wound inductors and parallel plate capacitors,wired together into a filter circuit. These conventional components arerelatively small compared to the wave length, and accordingly, make fora fairly compact filters. However, the use of separate elements hasproved to be difficult in manufacture, and resulting in large circuit tocircuit differences. The second conventional filter structure utilizesmechanical distributed element components. Coupled bars or rods are usedto form transmission line networks which are arranged as a filtercircuit. Ordinarily, the length of the bars or rods is ¼ or ½ of thewave length at the center frequency of the filter. Accordingly, the barsor rods can become quite sizeable, often being several inches long,resulting in filters over a foot in length. Third, printed distributedelement filters have been used. Generally they comprise a single layerof metal traces printed on an insulating substrate, with a ground planeon the back of the substrate. The traces are arranged as transmissionline networks to make a filter. Again, the size of these filters canbecome quite large. The structures also suffer from various responses atmultiples of the center frequency.

Various thin-filmed lumped element structures have been proposed.Swanson U.S. Pat. No. 4,881,050, issued Nov. 14, 1989, discloses athin-film microwave filter utilizing lumped elements. In particular, acapacitor π network utilizing spiral inductors and capacitors isdisclosed. Generally, a multi-layer structure is utilized, a dielectricsubstrate having a ground plane on one side of the substrate andmultiple thin-filmed metal layers and insulators on the other side.Filters are formed by configuring the metal and insulation layers toform capacitive π-networks and spiral inductors. Swanson U.S. Pat. No.5,175,518 entitled “Wide Percentage Band With Microwave Filter Networkand Method of Manufacturing Same” discloses a lumped element thin-filmbased structure. Specifically, an alumina substrate has a ground planeon one side and multiple layer plate-like structures on the other side.A silicon nitride dielectric layer is deposited over the first plate onthe substrate, and a second and third capacitor plates are deposited onthe dielectric over the first plate.

Historically, such lumped element circuits were fabricated using normal,that is, non-superconducting materials. These materials have an inherentloss, and as a result, the circuits have various degree of lossiness.For resonant circuits, the loss is particularly critical. The qualityfactor Q of a device is a measure of its power dissipation or lossiness.Resonant circuits fabricated from normal metals have Q's at best on theorder of a few hundred.

With the discovery of high temperature superconductivity in 1986,attempts have been made to fabricate electrical devices from thesematerials. The microwave properties of the high temperaturesuperconductors has improved substantially since their discovery.Epitaxial superconductive thin films are now routinely formed andcommercially available. See, e.g., R. B. Hammond, et al., “EpitaxialTl₂Ca₁Ba₂Cu₂O₈ Thin Films With Low 9.6 GHz Surface Resistance at HighPower and Above 77 K”, Appl. Phy. Lett., Vol. 57, pp. 825–827, 1990.Various filter structures and resonators have been formed. Otherdiscrete circuits for filters in the microwave region have beendescribed. See, e.g., S. H. Talisa, et al., “Low- and High-TemperatureSuperconducting Microwave Filters,” IEEE Transactions on MicrowaveTheory and Techniques, Vol. 39, No. 9, September 1991, pp. 1448–1554.

The need for compact, reliable narrow band filters has never beenstronger. Applications in the telecommunication fields are of particularimportance. As more users desire to use the microwave band, the use ofnarrow band filters will increase the number of users in the spectrum.The area from 800 to 2,000 MHZ is of particular interest. In the UnitedStates, the 800 to 900 MHz range is used for analog cellularcommunications. The personal communications services are planned for the1,800 to 2,000 MHZ range.

Many passive microwave devices, for example, resonators, filters,antennas, delay lines and inductors, have been fabricated in planar formutilizing high temperature superconducting thin films. As described,such structures are often smaller than conventional technologies interms of physical size. However, these devices are also limited in theirsize given the constraints of fabricating high quality, epitaxial films.As a result, devices fabricated in HTS films are often of a quasi-lumpedelement nature, that is, where the nominal size the device is smallerthan the wavelength of operation. This often results in folding ofdevices, which leads to significant coupling between lines.

Despite the clear desirability of improved electrical circuits,including the known desirability of converting circuitry to includesuperconducting elements, efforts to date have been less thansatisfactory in all regards. It has proved to be especially difficult insubstituting high temperature superconducting materials to form circuitswithout severely degrading the intrinsic Q of the superconducting film.These problems include circuit structure, radiative loss and tuning andhave remained in spite of the clear desirability of an improved circuit.

SUMMARY OF THE INVENTION

This patent relates to various novel structures and methods for forminghigh temperature superconducting devices, most particularly resonators.These devices have high Q, that is, at least in excess of 1,000, morepreferably in excess of 25,000, and most preferably in excess of 50,000.Generally, these inventive structures reduce peak current densitiesrelative to known structures. One significant result of reduced currentdensity is in reduced intermodulation effects. In one embodiment, asnake resonator includes a plurality of long runs, connected by aplurality of turns, wherein certain ones of the long runs are wider thancertain other ones of the long runs the wider runs being those thatwould have a higher current density if all runs were of equal width.

In one aspect of this invention, a spiral snake resonator having aterminal end disposed within the resonator is provided. In the preferredmode of this embodiment, multiple long runs are connected by turns,where the turns at one end of the resonator are concentric semicircles,with the center of radius being disposed between long runs. The turns atthe second ends of the resonator are also concentric semicircles, thoughwith the center of curvature being disposed at the end of a centrallydisposed long run.

In one specific preferred embodiment, a spiral snake resonator includesa plurality of N long runs, each one of the plurality of N long runshaving two ends and a plurality of turns connecting the plurality of Nlong runs to each other in a spiral snake configuration. The resonatoris characterized in that one end of a first long run of the plurality ofN long runs is connected to one end of a second long run of theplurality of N long runs by a first turn of the plurality of turns of afirst handedness, and the other end of the second long run is connectedto one end of a third long run of the plurality of N long runs by asecond turn of the plurality of turns of said first handedness, thethird long run being disposed between the first long run and the secondlong run, the remaining long runs of the plurality of N long runs beingby repeating the connections of the first, second and third long run forthe remaining plurality of N long runs using the remaining plurality ofturns starting at the other end of the third long run and terminating atone end of the Nth long run of the plurality of N long runs. Theresonator is further characterized by the feature that the plurality ofturns located at the first ends of the plurality of long runs areconcentric with each other around a center point disposed between longruns N and N−1 and wherein the plurality of turns located at the secondends of the plurality of long runs are concentric with each other arounda center point disposed on the end of the Nth long run.

Accordingly, it is an object of this invention to provide improved hightemperature superconducting structures.

It is yet a further object of this invention to provide improvedresonators having reduced intermodulation.

It is yet a further object of this invention to provide resonatorshaving reduced peak current densities.

It is yet a further object of this invention to provide high Q,superconducting resonators having reduced intermodulation effects.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a plan view of a quasi-lumped element resonator having wideinput and output pads in a serpentine or zig-zag inductor structure.

FIG. 2 is a plot of the current and voltage distributions of a ½wavelength resonator at its fundamental resonance frequency, plottedabove a ½ wavelength resonator structure.

FIG. 3 is a plan view of a zig-zag snake resonator having no significantinput and output pad structures.

FIG. 4 is a plan view of a spiral in, spiral out structure having nosignificant input and output pad structures.

FIG. 5 is a plan view of a spiral in, spiral out structure with inputand output pads.

FIG. 6 is a plan view of a spiral snake resonator having no significantinput and output pads.

FIG. 7 is the spiral snake resonator of FIG. 6 with the end portionsshown displaced from the linear portions of the structure.

FIG. 8 is a plan view of a lumped, spiral in, spiral out resonator witha wide in the middle structure.

FIG. 9 is a graph of the intermodulation product as a function of inputpower for the lumped element spiral in, spiral out resonator and thewide in the middle spiral in, spiral out resonator.

FIG. 10 is a emulation of a resonator utilizing an electromagneticsimulator.

FIG. 11 is a zig-zag resonator having nonuniform thickness lined widths.

FIG. 12 is a depiction of the electromagnetic simulation.

FIG. 13 is a output of an electromagnetic simulation.

FIG. 14 is a plot of the intermodulation power output as a function ofthe power input comparing a uniform zig-zag snake resonator with a “fat”zig-zag snake.

FIG. 15 shows resonate modes for an ideal straight resonator for fixedfrequency and stored energy (loaded Q) showing the reduction in peakenergy/current density when higher modes are employed.

FIG. 16 shows a graph of the intermodulation product versus input powerfor the fundamental and first harmonic of a spiral in, spiral outresonator.

FIG. 17 a is a plan view of a zig-zag or serpentine resonator at itsfirst harmonic and FIG. 17 b is a plan view of a wide at peaks resonatorat its first harmonic.

FIGS. 18 a, 18 b, 18 c and 18 d show outputs of electromagnetic modelsimulations for the magnitude in the fundamental mode (FIG. 18 a), thephase in the fundamental mode (FIG. 18 b), the magnitude in the firstharmonic mode (sometimes referred to as “ALF”) (FIG. 18 c) and the phasein that mode (FIG. 18 d).

FIGS. 19 a, 19 b, 19 c and 19 d show current density cross sections fora zig-zag, spiral in, spiral out, spiral and ALF spiral in, spiral outresonators using a planar 3D electromagnetic simulations packagedeveloped by US company Sonnet, Inc.

FIG. 20 shows a plan view of a hairpin resonator.

FIG. 21 a shows a graph of the unloaded Q (Q_(U)) as a function of gapwidth.

FIG. 21 b shows a graph of the intermodulation power P_(IMD) as afunction of gap width.

FIG. 22 shows a graph of the intermodulation power P_(IMD) as a functionof input power P_(IN) for a hairpin resonator.

FIGS. 23 a and 23 b show graphs of the current in the hairpin resonatorof FIG. 20 in the fundamental mode (FIG. 23 a) and the harmonic mode(FIG. 23 b).

FIG. 24 shows results of operation of a resonator of this invention.

FIG. 25 a illustrates a spiral in, spiral out resonator according to oneembodiment of the invention.

FIGS. 25 b and 25 c show results of operation of a resonator of thisinvention.

FIG. 26 illustrates a spiral in, spiral out resonator according to oneembodiment of the invention.

FIG. 27 shows a plan view of a filter utilizing a spiral in, spiral outstructures.

DETAILED DESCRIPTION OF THE INVENTION

FIG. 1 shows a plan view of a quasi-lumped element resonator (QLE)having enlarged input and output pads. An input pad 10 (the designationof input and output being arbitrary, and reversible) and an output pad16 are disposed on opposite sides of a serpentine or zig-zag resonatorregion 18. Generally parallel long runs 12 are disposed substantiallyparallel to the longer edge of the input pad 10 and output pad 16. Afirst long run 12 adjacent to the input pad 10 is connected to a firstturn 14 which electrically couples the input pad 10 to the first longrun 12. Adjacent long runs 12 are then coupled to their nearest neighborlong runs 12 by corresponding turns 14.

The input pads 10 and output pad 16 serve to increase the equivalentcapacitance to ground relative to a structure having no or smaller inputand output pads. Preferably, the amount of equivalent capacitance toground is selected in accordance with the electrical requirements of thecircuit. As shown in FIG. 1, the total area occupied by the input pad 10and output pad 16 exceeds that area occupied by the zig-zag resonatorregion 18.

The center frequency f_(c) of such a resonator isf_(c)∝1/√{square root over (LC)}wherein L is the inductance and C is the capacitance of the resonator. Acondition of resonance is that the energy stored in the magnetic fieldW₁ and the energy stored in the electric field W_(c) must be equal to:

$W = {W_{c} = {W_{I} = {{\frac{1}{2}{CV}^{2}} = {\frac{1}{2}{LI}^{2}}}}}$wherein V is the voltage and I is the current, and W is the energystored at resonance.

When the unloaded Q is much larger than the loaded Q, as is often thecase for superconducting filters, then the stored energy at resonance,W, is determined by the loaded Q. Thus, if the frequency and loaded Qare fixed, it is clear that in order to decrease the circulating currentwe must increase L, while simultaneously decreasing C to preserve theresonant frequency.

FIG. 2 shows the current and voltage distributions of a ½ wavelength(λ/2) resonator at its fundamental resonance frequency. A microstripformat may be utilized to implement a ½ wavelength transmission line.Such structures generally have inductance and capacitance which form theresonator distributed along the line 20. The current distribution insuch a structure at resonance is of the form sin(π×/1) having a maximumin the center of the resonator. The voltage distribution is of the formcos(π×/1) with maxima at the ends of the resonator.

FIG. 3 shows a plan view of a zig-zag or serpentine snake resonator 30.A first long run 31 is connected to a nearest neighbor long run 32 by aturn 36. In similar fashion, the third long run 33 is connected to thenearest neighbor long run 32 by turn 37. This pattern is repeated untilreaching a last long run 39.

FIG. 3 differs from FIG. 1 principally in that the input pad 10 andoutput pad 16 of FIG. 1 are eliminated or significantly reduced in size.By reducing the size of the capacitor pads 10, 16, the effectiveinductance of the quasi-lumped resonator is increased in FIG. 3 relativeto FIG. 1. For a fixed frequency and loaded Q, this implies that thecurrent density in the resonator can significantly be reduced by removalof the large capacitor pads. This has the effect of making theresonators behave more like folded distributed (½ wavelength)resonators. As an added current density reducing benefit, the linewidthof these resonators is usually higher than the linewidth at the highestcurrent point in their QLE counterparts.

To a first approximation, the unloaded Q of an HTS resonator isQ=wL/R_(s) where w is the resonant frequency and R_(s) is the surfaceresistance at that frequency. Thus, we see an additional advantage ofthese resonators over their QLE counterparts in terms of their higherunloaded Qs.

Using these structures, small area resonators can reliably beconstructed which have the following desirable properties.

Resonator Resonant IMD (Input Area Frequency Unloaded Q Loaded Q Power:−20 dBm) <1 cm² 850 MHZ >50,000 ~1000 <−80 dBc

FIG. 4 shows a plan view of a spiral in, spiral out snake resonator. Afirst long run 41 is connected to a second long run 48 by a first turn51. The first turn 51 has a preselected handedness, here taken to beleft-handed, though the designation of left and right-handed isarbitrary and therefore reversible. The second long run 48 is thenconnected by second turn 52, which is of the same handedness as is thefirst turn 51. The second turn 52 is connected to the third long run 43,which is then connected to turn 53 which is again of the same handednessof first turn 51 and second turn 52. The third turn 52 is connected tofourth long run 46, which is then connected to fourth turn 54, which isagain of the same handedness of the preseating turns 51, 52 and 53. Afifth long run 45 is connected to the fourth turn 54. The fifth long run45, being the center long run, namely, the line of symmetry for theresonator, then connects to a first turn of opposite handedness 61 whichin turn connects to a sixth long run 44. The run 44 connects to a secondturn of opposite handedness 62, which has the same handedness as thefirst turn of opposite handedness 61, which is opposite to thehandedness of the first turn 51. The second turn of opposite handedness62 connects to the seventh long run 47, which connects to the third turnof opposite handedness 63 which connects to the seventh long run 42,which connects to the fourth turn of opposite handedness 64 whichconnects to the ninth or last long run 49.

The spiral in, spiral out structure of FIG. 4 may be implemented withvarying number of long runs and turns. Generally, the following criteriadescribe the topology of the spiral in, spiral out structure. The spiralin, spiral out structure includes an odd number of long runs, identifiedto be N, where N is ≧5. Numbering the long runs sequentially from 1 toN, the first long run is connected to the N-first long run by a turn ofa first handedness. Long run N−1 is connected to long run 3 by a secondturn of first handedness. This sequence is repeated until a turn of thefirst handedness connects to long run (N+1)/2. Long run (N+1)/2 isconnected to long run (N+3)/2 by a turn of opposite handedness. Long run(N+3)/2 is connected by a second turn of opposite handedness to a longrun (N−3)/2. This process is repeated until the last long run (N) isreached.

FIG. 5 shows a plan view of a lumped element spiral in, spiral outresonator having enlarged input and output pads. In comparison to FIG. 4where nine long runs 40, 41 . . . 49 are utilized, FIG. 5 has seven longruns 71, 72, 73, 74, 75, 76, 77. The first long run 71 has an enlargedwidth relative to other runs, serving to have increased capacitance. Thefirst long run 71 is connected to first turn of first handedness 81 tothe sixth long run 76. The long run 76 is connected by the second turnof first handedness 82 to the third long run 73, which is in turnconnected by the third turn of first handedness 83 to the center longrun 74. The center long run 74 is connected in turn to first turn ofopposite handedness 84, which is connected to the fifth long run 75,which is connected to second turn of second handedness 85 to the secondlong run 72, which is in turn connected to the third turn of secondhandedness 86 to the last long run or output capacitor pad 77. Theoutput capacitor pad 77 has a width which is enlarged relative to theother interior long runs, and is shown having the same width as thefirst input capacitor pad or long run 71.

FIG. 6 shows a plan view of a spiral snake resonator 90. A first longrun 91 is connected to a second long run 92 by a first turn 101. Thesecond long run 92 is connected to a third long run 93 which is disposedbetween the first long run 91 and the second long run 92, by a secondturn 102. Second turn 102 has the same handedness as first turn 101.Third long run 93 is connected to a fourth long run 94 which is disposedbetween the second long run 92 and the third long run 93. The third turn103 has the same handedness as the first turn 101 and second turn 102.This structure is repeated starting at a fourth turn 104 connected tothe fourth long run 94 until terminating in a last long run 95 which iscentrally disposed between the first long run 91 and second long run 92.

FIG. 7 shows a spiral snake resonator with the turn portions(corresponding to 101, 102, 103 and 104 of FIG. 6) physically displacedfrom the long runs (91, 92 . . . 95 of FIG. 6) for clarity. Inoperation, these portions would be connected as shown in FIG. 6. FIG. 7differs from FIG. 6 in that it includes seven long runs, as opposed tonine long runs for FIG. 6. Adopting the same number scheme as for FIG.6, FIG. 7 shows that the even numbered turns 102, 104, disposecollectively at one end of the long runs, are concentric with each otheraround a point 110. Turns 101, 103 disposed on the right hand side ofthe long runs are concentric with each other around a point 112. Thecenter of radius 112 is disposed on the end of the last long run 95. Incontrast, the center of curvature 110 is disposed at the end of andbetween the last long run 95 and the preceding last long run. If thereare N long runs, and the numbering convention is to sequentially numberthe long runs beginning with the outermost long run, the center point110 is disposed between long runs N and N−1.

FIG. 8 shows a plan view of a spiral in, spiral out resonator having awide portion in the middle region. The spiral in, spiral out aspects ofFIG. 8 are as previously described in connection with FIG. 4. Incontrast, FIG. 8 includes a center long run 120 (compared to the centerlong run 45 in FIG. 4) which is relatively wider than other long runs122. The structure of FIG. 8 generally comprises a quasi-lumped elementresonator structure particularly useful for bandpass and band rejectfilters. In the fundamental resonant mode, the peak circulating currentslie in the center of the resonator. Broadening the center conductor 120increases the cross-sectional area of the transmission line, whichallows for greater current transport. Generally, it is believed thatthis technique serves to alleviate the stress of large peak currents.The width of the center conductor 120 in FIG. 8 is six times as wide asthe remaining conductor 122. However, resonators in which the width ofthe center long run 120 is at least twice as wide as the remaining longruns would utilize the concept of this invention.

FIG. 9 shows the intermodulation product (P_(IMD,out)) as a function ofinput power (P_(in)) for the structure of FIG. 5 (labeled LESISO forlumped element spiral in, spiral out) and the structure of FIG. 8(labeled WIMSISO for wide in middle spiral in, spiral out). As can beseen, for a given power input, the wide in middle spiral in, spiral outresonator of the type shown in FIG. 8 has lower intermodulation comparedto the lumped element spiral in, spiral out structure of FIG. 5.

FIGS. 10, 11, 12 and 13 relate to graduated line width structures. FIG.11 shows a zig-zag or serpentine resonator structure, but where thewidth of the conductors vary as a function of position within theresonator. External long runs 120 are relatively thinner than adjacentlong runs 122, which are in turn thinner than next adjacent long runs124, which are yet in turn relatively thinner than adjacent long runs126. The center long run 128 is preferably larger than the remaininglong runs.

Broadly, the technique disclosed herein is for increasing the line widthof a folded HTS resonator as a function of current density. Consideringa structure such as FIG. 3 with uniform width long runs 32 and uniformgaps between adjacent long runs, e.g., long run 32 and long run 34, ifstraightened out, would resemble a half wave resonator, assuming thefundamental mode. In this situation, the current distribution along thelength of the resonator would be sin (Qπ×/λ).

FIG. 10 shows a technique for simulating the resonator of the form shownin FIG. 11. If the resonator is considered to comprise long parallelruns, each having the same length, without consideration of the turns,the currents in the individual lines I_(i) in terms of the maximum orminimum current (I_(max),I_(min)) in a segment is as follows:

i I_(i)/I_(max) I_(i)/I_(min) Adjacent Leg Ratio 1 0.158384338 1 — 20.459649276 2.902113197 2.902113197 3 0.715920617 4.5201478091.557536699 4 0.902112776 5.695719602 1.26007375 5 1 6.313755611.108508854 6 0.902112776 5.695719602 1.26007375 7 0.7159206174.520147809 1.557536699 8 0.459649276 2.902113197 2.902113197 90.158384338 1 —

Ideally, the structure of the graduated resonators would be smoothlines, such as shown in the smooth lines of FIG. 13. In certainapplications (such as a linear, non-folded structure) it may bedesirable to have the shape follow some power of the currentdistribution. However, when folding the resonators into the variousdisclosed shapes, e.g., spiral in, spiral out, zig-zag or snake,modified spiral, utilizing continuous change in the line width generallyresults in lines which are not parallel. By utilizing the generallyparallel structures disclosed as the preferred embodiments herein, wherethe spacing between adjacent long runs may be made constant, modeling ofsuch systems is made easier. However, devices utilizing the concepts ofthese inventions may be implemented where line widths vary continuouslyat some or all of the portions of the resonator.

Preferably, the ratio of widths from outside of long runs 120 at theends of the resonator to adjacent segments is 1:3. However, undercertain circumstances, this can create an impedance mismatch whichbecomes significant, and for practical size requirements utilizingcurrent processing technology makes the width of the long runs too smallor fine.

FIG. 12 shows a modeling of a structure of FIG. 11 where the ratiobetween adjacent long runs 120, 122 is 2:3. Thus, to build a equivalent9 long run zig-zag resonator with 0.3 millimeter lines and gaps, thetotal width is distributed over the lines as follows, numbers 6–9mirroring 4–1:

i Ideal Realization Width (mm) Gap (mm) 1 1 2 .146 .1825 2 3 3 .219.27375 3 4.5 4.5 .3285 .365 4 5.5 5.5 .4015 .41975 5 6 6 .438

Alternatively, the circuit may be modified in other ways. For example,if the circuit were split into three segments, as opposed to the ninesegments described previously, the values would be approximately asfollows:

i Ideal Realization Width (mm) Gap (mm) 1 1 1 .243 .243 2 1 1 .243 .2433 1 1 .243 .3645 4 2 2 .486 .486 5 2 2 .486

FIG. 13 shows a modeling where the width of the long runs is varied as afunction of a higher power of the current density. Under certainconditions, this arrangement may increase impedance mismatch at the endsof the resonator without any appreciable effect in the central region ofthe resonator where the currents are largest.

FIG. 14 shows a graph of the intermodulation performance P_(IMD, OUT) asa function of input power for a zig-zag or serpentine resonator as shownfor example in FIG. 3 and a resonator having varying thickness long runsas shown for example in FIG. 11. The resonators have substantially equalresonator area, that is, they occupy substantially the same amount ofoverall area on a HTS film. FIG. 14 shows the structure of FIG. 11(labeled “FAT” zig-zag snake) has a reduction of up to 5 dB inintermodulation product as compared to the structure of FIG. 3 (labeleduniform zig-zag snake).

FIG. 15 shows four resonators 130, 132, 134 and 136. Shown above thoseresonators is a graphic indicating the current as a function of positionwithin the resonator. For ½ wavelength resonator 130, for a givenresonant frequency and stored energy, the current distribution along theresonator is shown by line 130′. Similarly, clearly, for resonator 132,when in the next mode number (mode 1 where mode 0 is the lowest ordermode) is shown by line 132′. Similarly, for resonator 134, when in thenext mode number (mode 3), the current distribution along the resonatoris shown by line 134′. Finally, for resonator 136, when in the next modenumber (mode 4), the current distribution along the resonator is shownby line 136′. For a given resonant frequency and stored energy, the peakenergy density is inversely proportional to the mode number. Utilizinghigher modes serves to reduce the stress placed upon the resonator, andreduces intermodulation products. This discovery may be utilized inconnection with any of the ½ wavelength resonators described herein.

FIG. 16 shows a plot of the intermodulation product P_(IMD, OUT) as afunction of input power for the fundamental and first harmonic of aspiral in, spiral out resonator (See e.g., FIGS. 4 and 5). As can beseen, the first harmonic has lower intermodulation product as comparedto the fundamental harmonic.

FIG. 17 b shows a zig-zag or snake resonator operable at a firstharmonic, where FIG. 3 in comparison would show a zig-zag or snakeresonator at the fundamental frequency. If it is desired to preserve thecircuit area, but to use the first harmonic as in FIG. 17 b as comparedto the fundamental in FIG. 3, the width of the long runs is reduced,preferably halved, in order to double the electrical length of theresonator. FIG. 17 b shows a resonator operable at a first harmonic andutilizing the wide at peak structure described in conjunction with FIGS.15 and 16, above. Thus, the structure of 17 b when operated at the firstharmonic has two regions corresponding to the relatively wider regionsof the long runs at which the current density is reduced. This wide atpeaks resonator structure advantageously improves the intermodulationperformance. The principals of the wide at peaks technique may also beapplied to spiral in, spiral out snake resonators. In such resonators,due to the nature of the spiral in, spiral out folding, the oddharmonics of the resonator are closer to that of a spiral resonator inits fundamental mode.

FIGS. 18 a and 18 b show the magnitude and phase, respectively, on amodeled system of a spiral in, spiral out resonator. The modeledstructure is based upon a resonator of the structure shown in FIG. 4 anddescribed above. As shown, the system is modeled as having ‘singleturns’ which are linear and substantially parallel to adjacent ‘turns’.While this structure is advantageously utilized for modeling, it mayalso be utilized in physical implementations of the structures. Indeed,the structures described herein may be utilized with round or roundedturns, squared turns, mitred turns, or any turn serving as aninterconnection between the long runs which does not materiallynegatively impact the achieving the goals or objects of theseinventions. One source for modeling software is Sonnet Software, Incs.,Suite of Planar 3DEM Tools (referred to either as “Sonnet” or “em”) andis available from Sonnet Software, Inc., 10207 North Street, Suite 210,Liverpool, N.Y. 13088. The magnitude shown in FIG. 18 a increases fromthe ends of the resonators to a maximum value in the middle of thecenter line. The frequency of modeling is 0.71742 GHz. The phase showsthat segments in the odd numbered long runs (40, 43, 45, 47, and 49 inFIG. 4 and also in FIGS. 18B and 18D) have a phase substantially 180°opposite to that of the even numbered long runs (40, 42, 44, 46 and 48in FIG. 4 and also in FIGS. 18B and 18D).

FIGS. 18 c and 18 d show the magnitude and phase respectively for thesimulation of the same spiral in, spiral out resonator but at the firstharmonic. The magnitude shows that the magnitude rises from the ends ofthe resonator to two peaks situation roughly at ¼ and ¾ of the length ofthe line, with the magnitude decreasing from the peaks to the center ofthe resonator. The phase shown in FIG. 18 d shows that the resonator insubstantially the upper half is of one phase, whereas the resonator insubstantially the bottom half is of 180° phase difference. The phasechange is at substantially the center of the middle long run (long run45 in FIG. 4).

It has been discovered that the use of a symmetric mode, that is, one inwhich currents flow in the same direction in adjacent legs of theresonator, such as is shown in FIG. 18 b, provide superior results.Specifically, the use of the symmetric mode serves to reduce currentdensities relative to the asymmetric mode. One of the direct beneficialresults of reduction in current density is the reduction inintermodulation effects. While the asymmetric mode, that is, one inwhich currents flow in opposite directions in adjacent legs of theresonator, are beneficial respecting far field shielding, if the farfield effects can be pushed sufficiently away the symmetric mode has thebenefit described previously.

Experimental Results

The following table provides data regarding spiral resonators, andspiral in, spiral out snake resonators of the size and area identified.

Topology Spiral Spiral SISO Snake SISO Snake SISO Snake SISO SnakeLength [mm] 10.41 10.41 8.8175 8.8175 16.25 16.37 Width [mm] 4 4 6.4 6.43.6009 7.0025 Area [cm²] 0.4164 0.4164 0.56432 0.56432 0.585146251.14630925 LineWidth [mm] 0.4 0.4 0.4 0.4 0.4 1 Gap [mm] 0.2 0.2 0.2 0.20.4 0.5 Frequency [MHZ] 829.285 829.5 849.291 849.19 865.866 869.206Unloaded Q 39800 37700 27200 37000 53500 65300 Loaded Q 4130 4000 41304610 3570 3440 IMD @-20 dBm[dBc] −55.5 −76 −62.5 −58.5 −66 −69 IMD @-20dBm [dBc] −80.1 −100.1 −87.1 −85.0 −88.1 −90.5 (QL~1000)

FIGS. 19 a, 19 b, 19 c, 19 d show Sonnet current density cross-sectionsfor zig-zag, spiral in, spiral out, spiral and higher mode (ALF) spiralin, spiral out resonators. Specifically, FIGS. 19 c and 19 d showquantitative results for a resonator cut line in a vertical directionsuch as labeled on cut 19 in FIG. 18 a and FIG. 18 b. Thus, for thespiral in, spiral out structure in the fundamental mode (FIGS. 18 a and18 c and lower left figure in FIG. 19 c labeled SISO) the currentdensity can be seen to alternate in direction from adjacent long runs.Thus, in FIG. 19 c SISO, the external most long runs correspond tovalues 141, 149, the adjacent long runs corresponding to values 142,148, 143, 147, 144 and 146 to the value 145 of the center resonator. Ascan be seen, the current is opposite directions for adjacent lines(compare the positive value of 141 with the negative value of 142). Inthe higher mode spiral in, spiral out resonator (FIGS. 18 b and 18 d andlower right graph in FIG. 19 d labeled ALF SISO), again utilizing thesame number convention, shows that adjacent resonators corresponding tovalues 151, 152, 153 and 154 are all negative, indicating current flowin the same direction. In contrast, current in long runs correspondingto values 156, 157, 158 and 159 run in the same direction, thatdirection being opposite to the direction of current in the long runscorresponding to values 151, 152, 153 and 154. As shown, the value 155corresponding to the center resonator is shown substantially at 0. Ascan be seen in the graphics of FIG. 19 d, the current shows divergencesat the edges of the long runs of the resonator. Further, while the ALFSISO of FIG. 19 d is at a higher frequency (then a harmonic) as comparedto the fundamental frequency such as used in the SISO of FIG. 19 c, theALF SISO shows a lower envelope, corresponding to lower current densityas compared to the other structures shown.

FIG. 20 shows a plan view of a hairpin resonator 160. The hairpinresonator 160 is characterized in having a first long run 162 having alength L and a width W, and a second long run 164, also having a lengthL and width W, the first long run 162 and second long run 164 beingsubstantially parallel to each other, and separated by a gap G. The longruns 162, 164 are connected to turn 166. The hairpin resonator 160 isspaced a distance S from conductor 168, and is generally parallel to thelong runs 162, 164. It has been discovered that the particularlygeometry affects both the losses and intermodulation in theseresonators. The first harmonic mode gives less intermodulation relativeto the fundamental mode, though the first harmonic mode has relativelyhigher losses relative to the fundamental mode, believed to be due tothe more extended fields of that mode. In operation, microwave energymay be coupled to these resonators in a band reject fashion via thetransmission line 168. The spacing S between the transmission line 168and the resonator 160 determines the strength of the coupling and thusthe energy stored in the resonator, which may be characterized in termsof the loaded quality factor Q_(L) of the device.

The response of the band reject resonator may be characterized in termsof three quantities, the resonance frequency, F₀, and the loaded andunloaded quality factors, Q_(L) and Q_(U), respectively. F₀ and Q_(L)are determined by the geometry of the resonator 160 and substrate.

For the actual experiments performed, the width of the runs 162, 164 wasfixed at 0.4 mm, with L, G and S being adjustable parameters. Theresonance frequency of 7.4 GHz was chosen.

FIG. 21 a shows a graph of the unloaded quality factor (Q_(u)) of thegap g for a series of hairpin resonators. The experimental results forthe symmetric resonators (second mode, represented by circles), theantisymmetric resonators (first mode, represented by squares) and thestraight resonator (represented by triangles) are compared withnumerical calculations (solid, long-dashed, and short-dashed line,respectively). The dotted line accounts for the losses in the lid forthe symmetric resonators.

FIG. 21 b shows a graph of the intermodulation power P_(IMD) measured indecibels as a function of gap g for a series of hairpin resonators. Theexperimental results for the symmetric resonators (second mode,represented by circles), the antisymmetric resonators (first mode,represented by squares) and the straight resonator (represented bytriangles) are compared with numerical calculations (solid, long-dashed,and short-dashed line, respectively). The open symbols represent the rawdata as measured before correction to {tilde over (Q)}=1700. Theintermodulation power is measured in decibels referenced to 1 mW.

FIG. 22 shows a graph of the intermodulation power P_(IMD) for a hairpinresonator as a function of the input power P_(IN) of the fundamentalsignals. Both powers are measured in decibels referenced to 1 mW. Inset:P_(IMD) as a function of {tilde over (Q)}=Q_(L)(1−Q_(L)/Q_(U)). The dataare consistent with the theoretical expected P_(IMD)∝{tilde over (Q)}⁴.

FIG. 23 a shows a graph of the current in the hairpin resonator of FIG.20 in the fundamental mode. The current can be seen to flow in oppositedirections in adjacent legs of the hairpin resonator 160. FIG. 23 bshows the current distribution in the hairpin resonator 160 in theharmonic mode. The current can be seen to run in the same direction inadjacent long runs 162, 164, thus operating in the symmetric mode.

Four sets of resonators were designed:

-   -   1. For gap widths of g=0.4, 0.2, 0.1 and 0.05 mm, L (long run        length) and S (spacing from conductor) were adjusted so that the        first resonance was at f₀=7.4 GHz with Q_(L)=2000, resulting in        L˜4 mm and S˜1 mm. As the microwave currents flow in opposite        directions in the two legs of the resonator these will also be        referred to as anti-symmetric resonators.    -   2. For gap widths of g=0.4, 0.2, 0.1 and 0.05 mm, L and S were        adjusted so that the second resonance was at f₀=7.4 GHz with        Q_(L)=2000, resulting in L˜7 mm and S˜2 mm. Since the currents        flow in the same direction in the two legs of the resonator        these will be referred to as symmetric resonators.    -   3. For a gap width of g=0.4 mm, L and S were adjusted so that        the second resonance remained at f₀=7.4 GHz but the coupling        strength varied at Q_(L)=2000, 1000, 500, 200.    -   4. A straight resonator was designed so that its first resonance        was at f₀=7.4 GHz with Q_(L)=2000, resulting in L˜7.7 mm and S˜2        mm.

The circuits were clipped into gold plated test fixtures using Indiumfoil below the circuit to ensure proper thermal and electrical contact.The microwave circuit was then completed by wire bonds at both ends ofthe 50 Ω thru line. Note that the electrical ground plane seen by theresonator is, for the most part, provided by the unpatterned film on theback side of the substrate.

The microwave transmission characteristics, S21, were measured using HP8720B Vector Network Analyzer in order to determine f₀, Q_(U) and Q_(L)which characterize the linear response of the circuit at low microwavepowers. The Qs are obtained from direct measurements of the fractionalbandwidths at −3 dB, Δf_(−2 dB), the insertion loss, S₂₁(f₀), and thewidth of the resonance 3 dB above the minimum, Δf_(+3 dB). In all casesthe input power to the resonators was held fixed in P_(IN)=−20 dBm.

The measured and calculated Qs are presented in FIG. 21A. In thecalculations a surface resistance of R_(s)=210 μΩ at 7.4 GHz and apenetration depth of λ(77K)=0.3 μm were used.

For the antisymmetric resonators the calculations are in good agreementwith the measurements. For smaller gap sizes Q_(U) is degraded. This canbe understood from the antiparallel currents running in the gap region.Therefore, high current densities have to flow at the inner edges of thelegs to screen out this field from the superconducting films. These highcurrent densities lead to increased losses and to higherintermodulations. In contrast, for the symmetric mode the parallelcurrents lead to fields that cancel within the gap and no suchdegradation is expected. For this mode we find almost exactly doublewhat is measured (the dotted line shows half of the calculated values),using the same surface impedances used to evaluate the anti-symmetricmode Qs.

The circuits were tested with and without an Aluminum lid placed 0.150inches above the circuit. For the first set of resonators the effect ofremoving the lid was only a slight shift in the resonant frequency withno detectable change in Q_(U) or Q_(L). For the resonators which madeuse of the first harmonic (sets 2 and 3), the effect was far moresevere; there Q_(U) dropped close to an order of magnitude as the lidwas removed. This is an indication that the microwave fields associatedwith the resonator are far more extended for the symmetric modes thanfor the anti-symmetric ones.

The two microwave signals required to produce intermodulation productswere symmetrically placed 15 kHz above and below f₀, for a signalseparation of 30 kHz. Continuous Wave (CW) Signals were produced usingHP 8341B and HP 83640A synthesized sweepers, and the signals detectedusing a Tektronix 3784 Spectrum Analyzer. The output power of the twosources was measured using an HP 437B power meter, and adjusted so thatthe two signals arrived at the sample with the same magnitude.

The absolute magnitude of third order intermodulation products. P_(IMD),as a function of input power provided to the device, P_(IN) wasmeasured. For the 30 kHz signal separation we are using here thesesignals are generated at f₀±45 kHz. As can be seen in FIG. 22, P_(IMD)has a slope much closer to 2:1 (dotted line) than the 3:1 (dashed line)expected from a pure third order nonlinearity.

P_(IMD) at a fixed input power of P_(IN)+−20 dBm is presented as afunction of gap width for the first two sets of resonators and thestraight one in FIG. 21 b. P_(IMD) was set to Q=1700 using theintermodulation value as proportional to the fourth power of Q. The opensymbols denote the raw data while the full ones denote the adjustedvalues.

FIG. 24 shows the frequency response of the S-parameter for thefundamental resonance of a spiral snake resonator shown in an inset. Thesubstrate thickness was 0.020″. The dimensions of the resonance thusrealized are 3.3 mm by 6.7 mm, which is shown in the inset. The measuredunloaded quality factor was 101450 at 845.318 MHz at a temperature of77K.

FIG. 25 a shows a spiral in, spiral out snake resonator. When realizedwith YBCO films deposited on 0.015″ thick MgO substrates the resonatorwas 5.2 mm by 10.4 mm in area. The average unloaded quality factor ofthese resonators was measured to be 110,000 at a resonance frequency 845MHz and a temperature of 77K.

FIG. 25 b shows the measured frequency response of the S-parameters fora quasi elliptic band reject filter realized using six of the resonatorsin FIG. 25 a.

FIG. 25 c shows a simulation of the filter in 25 b taking the averagemeasured unloaded quality factor into account. The unloaded qualityfactor is apparent in the depth of the nulls as well as the sharpness inthe corners of the filter.

FIG. 26 shows an spiral-in-spiral-out resonator with moderately enlargedcapacitor pads. When realized using TBCCO films deposited on 0.020″LaAlO₃ the resonator is 7.7 mm by 10.4 mm in area. When operated in the“ALF” mode, the resonant frequency of this resonator is 846.477 MHz, andthe resonator had a measured unloaded quality factor of 150,050 at atemperature of 77K.

FIG. 27 shows a plan view of a filter structure having a plurality ofspiral in, spiral out structures 170, with side coupling therebetween.An input 172 and an output 174 provide signal coupling to the filterstructure.

Although the foregoing invention has been described in some detail byway of illustration and example for purposes of clarity andunderstanding, it may be readily apparent to those of ordinary skill inthe art in light of the teachings of this invention that certain changesand modifications may be made thereto without departing from the spiritor scope of the appended claims.

1. A snake resonator, comprising: a plurality of N long runs, each oneof the plurality of N long runs having two ends; and a plurality ofturns connecting the plurality of N long runs to each other in a spiralsnake configuration, characterized in that one end of a first long runof the plurality of N long runs is connected to one end of a second longrun of the plurality of N long runs by a first turn of the plurality ofturns, the other end of the second long run is connected to one end of athird long run of the plurality of N long runs by a second turn of theplurality of turns, the remaining long runs of the plurality of N longruns being by repeating the connections of the first, second and thirdlong run for the remaining plurality of N long runs using the remainingplurality of turns starting at the other end of the third long run andterminating at one end of the Nth long run of the plurality of N longruns; wherein certain ones of the long runs are wider than certain otherones of the long runs, the wider runs being those that would have ahigher current density if all runs were of equal width.
 2. The snakeresonator of claim 1 wherein there are three long runs.
 3. The snakeresonator of claim 1 wherein there are four long runs.
 4. The snakeresonator of claim 1 wherein N is
 5. 5. The snake resonator of claim 1wherein N is
 7. 6. The snake resonator of claim 1 wherein N is
 9. 7. Thesnake resonator of claim 1 wherein N≧9.
 8. The snake resonator of claim1 wherein the plurality of N long runs are substantially parallel toeach other and the spacing between adjacent long runs of the pluralityof N long runs is substantially constant.
 9. The snake resonator ofclaim 8 wherein a ratio of the width between at least two adjacent longruns of the plurality of N long runs is approximately 2:3.
 10. The snakeresonator of claim 1 wherein the plurality of N long runs aresubstantially parallel to each other and a ratio of the width between atleast two adjacent long runs of the plurality of N long runs isapproximately 2:3.
 11. The snake resonator of claim 1 wherein the snakeresonator has a fundamental resonant frequency and the snake resonatordefines an electrical length substantially equal to ½ the wavelength ofthe fundamental resonant frequency.
 12. The snake resonator of claim 1wherein the resonator has a Q of at least 1,000.
 13. The snake resonatorof claim 1 wherein the resonator has a Q of at least 10,000.
 14. Thesnake resonator of claim 1 wherein the resonator has a Q of at least50,000.
 15. The snake resonator of claim 1, wherein the plurality of Nlong runs and the plurality of turns are comprised of a high temperaturesuper conducting material.
 16. The snake resonator of claim 15 whereinthe high temperature superconducting material is a thallium containingsuperconductor.
 17. The snake resonator of claim 15 wherein the hightemperature superconducting material is a YBCO high temperaturesuperconductor.
 18. The snake resonator of claim 1 wherein the pluralityof N long runs and turns are formed in a thin film disposed on asubstrate.
 19. The snake resonator of claim 18 wherein a ground plane isdisposed on the substrate.
 20. The snake resonator of claim 1 whereinthe snake resonator is a spiral-in, spiral-out resonator.
 21. A snakeresonator, comprising: a plurality of N long runs, each one of theplurality of N long runs having two ends; and a plurality of turnsconnecting the plurality of N long runs to each other in a snakeconfiguration, characterized in that one end of a first long run of theplurality of N long runs is connected to one end of a second long run ofthe plurality of N long runs by a first turn of the plurality of turns,the other end of the second long run is connected to one end of a thirdlong run of the plurality of N long runs by a second turn of theplurality of turns, the remaining long runs of the plurality of N longruns being by repeating the connections of the first, second and thirdlong run for the remaining plurality of N long runs using the remainingplurality of turns starting at the other end of the third long run andterminating at one end of the Nth long run of the plurality of N longruns, wherein the plurality of N long runs are substantially parallel toeach other and a ratio of the width between at least two adjacent longruns of the plurality of N long runs is approximately 2:3; whereincertain ones of the long runs are wider than certain other ones of thelong runs, the wider runs being those that would have a higher currentdensity if all runs were of equal width.
 22. The snake resonator ofclaim 21 wherein the snake resonator is a spiral-in, spiral-outresonator.
 23. The snake resonator of claim 21 wherein the snakeresonator is a zig-zag resonator.
 24. The snake resonator of claim 21wherein there are three long runs.
 25. The snake resonator of claim 21wherein there are four long runs.
 26. The snake resonator of claim 21wherein N is
 5. 27. The snake resonator of claim 21 wherein N is
 7. 28.The snake resonator of claim 21 wherein N is
 9. 29. The snake resonatorof claim 21 wherein N≧9.
 30. The snake resonator of claim 21 wherein thespacing between adjacent long runs of the plurality of N long runs issubstantially constant.
 31. The snake resonator of claim 21 wherein thesnake resonator has a fundamental resonant frequency and the snakeresonator defines an electrical length substantially equal to ½ thewavelength of the fundamental resonant frequency.
 32. The snakeresonator of claim 21 wherein the resonator has a Q of at least 1,000.33. The snake resonator of claim 21 wherein the resonator has a Q of atleast 10,000.
 34. The snake resonator of claim 21 wherein the resonatorhas a Q of at least 50,000.
 35. The snake resonator of claim 21, whereinthe plurality of N long runs and the plurality of turns are comprised ofa high temperature super conducting material.
 36. The snake resonator ofclaim 35 wherein the high temperature superconducting material is athallium containing superconductor.
 37. The snake resonator of claim 35wherein the high temperature superconducting material is a YBCO hightemperature superconductor.
 38. The snake resonator of claim 21 whereinthe plurality of N long runs and turns are formed in a thin filmdisposed on a substrate.
 39. The snake resonator of claim 38 wherein aground plane is disposed on the substrate.
 40. The snake resonator ofclaim 21 wherein the snake resonator is a spiral resonator.